Lightly brush or spray the unpeeled shallot with olive oil.

Grill the shallot over direct medium heat until blackened and soft (about 15 minutes), turning once.

Remove the shallot from the grill and let it cool.

Remove and discard the peel from the cooled shallot.

Finely chop the roasted shallot.

In a medium bowl, combine the chopped shallot with balsamic vinegar, Dijon mustard, thyme, salt, and pepper.

Whisk in the remaining olive oil to create a smooth vinaigrette.

Trim any excess fat from the lamb racks.

Let the lamb stand at room temperature for 20-30 minutes.

Lightly brush or spray the lamb with olive oil.

Season the lamb with thyme, salt, and pepper.

Loosely cover the bones of the lamb with foil.

Sear the bone side of the lamb down over direct medium heat until lightly browned (2-4 minutes), turning once.

Move the lamb over indirect medium heat and grill to desired doneness (about 15 minutes more for medium-rare).

Remove the lamb from the grill and let it rest for 5 minutes.

Cut the rack of lamb into chops.

Serve the warm lamb chops with the roasted-shallot vinaigrette.